The present invention relates to digital signal processing, and more particularly to Fourier-type transforms.
Processing of digital video and audio signals often includes transformation of the signals to a frequency domain. Indeed, digital video and digital image coding standards such as MPEG and JPEG partition a picture into blocks and then (after motion compensation) transform the blocks to a spatial frequency domain (and quantization) which allows for removal of spatial redundancies. These standards use the two-dimensional discrete cosine transform (DCT) on 8×8 pixel blocks. Analogously, MPEG audio coding standards such as Levels I, II, and III (MP3) apply an analysis filter bank to incoming digital audio samples and within each of the resulting 32 subbands quantize based on psychoacoustic processing; see FIG. 3a. FIGS. 3b-3c show the decoding including inverse quantization and a synthesis filter bank.
Pan, A Tutorial on MPEG/Audio, 2 IEEE Multimedia 60 (1995) describes the MPEG/audio Layers I, II, and III coding. Konstantinides, Fast Subband Filtering in MPEG Audio Coding, 1 IEEE Signal Processing Letters 26 (1994) and Chan et al, Fast Implementation of MPEG Audio Coder Using Recursive Formula with Fast Discrete Cosine Transforms, 4 IEEE Transactions on Speech and Audio Processing 144 (1996) both disclose reduced computational complexity implementations of the filter banks in MPEG audio coding.
However, these known methods have high memory demands for their low- complexity computations.